RMSamplitude

RMS amplitude, short for root-mean-square amplitude, is a statistical measure used to quantify the magnitude of a varying signal. It provides a single representative value for the power content of a waveform, accommodating both positive and negative excursions.

Mathematically, the RMS amplitude is the square root of the mean of the squares of the signal values over a specified interval. For a continuous-time signal x(t) observed over a time T, the RMS amplitude is xrms = sqrt(1/T ∫_0^T [x(t)]^2 dt). For a discrete-time signal x[n] with N samples, it is xrms = sqrt(1/N ∑_{n=0}^{N-1} [x[n]]^2). If the signal is periodic, the interval can be one period. The RMS value is always nonnegative. A signal with a nonzero mean has an RMS larger than its mean, since xrms^2 = mean(x^2) = variance(x) + [mean(x)]^2.

In electrical engineering, RMS values relate to power: for a resistor R, the average power equals (Vrms)^2 / R. For a sinusoidal voltage with peak amplitude A, Vrms = A/√2. The crest factor, the ratio of peak amplitude to RMS, characterizes waveform sharpness.

RMS amplitude is widely used to quantify signal level in audio, telecommunications, and measurement. It differs from other measures such as the absolute mean or peak amplitude and depends on the chosen time window or interval. For non-stationary or time-varying signals, moving or windowed RMS calculations are common to track level changes over time.